As discussed by Becker et al., in a paper “Boron, The New Graphene?” in Vacuum Technology & Coating, April 2015, pp. 38-44, boron supports a unique and mysterious chemistry that has greatly perplexed scientists for many years in the pursuit of useful commercial applications that continue to defy a full chemical understanding. As further discussed in this article, there is an increasing belief by many scientists that new boron compounds could possibly exist in allotropes or polymorphs similar to, and superior to, the recently discovered carbon allotropes comprising fullerenes, carbon nanotubes, and graphene.
Boron is a light electron-deficient element with a small interatomic space between natural boron atoms supporting one shared molecular bonding orbital and two shared molecular antibonding orbitals amongst three boron atoms. As the result of this property, boron atoms tend to form three-center chemical bonds such that two valence electrons bond three boron atoms, with the peak electron density being in the center of the triangle comprised by three boron atoms. This type of chemical bond is very different from a two-center chemical bond in which the peak electron density exists along the rectilinear axis joining two valence electrons. Although boron is a Group-III element, it does not chemically act like other Group-III elements. Boron acts like a nonmetal and forms an extended series of hydrides.
Due to three-center bonds, boron tends to form polyhedral molecules comprising triangular faces. The highest-order symmetrical regular polyhedron formed by triangular faces is an icosahedron with twenty equilateral triangular faces that are interconnected by thirty edges so as to result in twelve vertices. Each vertex of a boron icosahedron is occupied by a boron atom with three valence electrons, such that conventional two-center chemical bonds cannot exist along the 30 icosahedral edges. In a boron icosahedron, the coordination number exceeds the number of boron valence electrons so as to result an electron deficiency. Similar to buckminsterfullerene C60, boron icosahedra can potentially form a cage-like molecule, but, boron icosahedra, because they are formed by only triangular faces, can display a higher symmetry than the truncated icosahedral buckminsterfullerene molecule formed by 20 hexagonal faces and 12 pentagonal faces.
In a key landmark paper, “The Electronic Structure of an Icosahedron of Boron,” Proceedings of the Royal Society, A230, 1955, p. 110, Longuet-Higgins and Roberts developed the molecular bonding conditions of a closed-shell boron icosahedron exhibiting an icosahedral symmetry Ih with a boron nucleus at each vertex. Longuet-Higgins and Roberts obtained the 48 molecular orbitals of a boron icosahedron by the linear combination of 48 nonorthogonal atomic orbitals that are related to 48 symmetry orbitals in terms of the irreducible representations of the regular icosahedral group Ih comprising the nondegenerate (Ag) irreducible representation along with threefold (T1u, T1g, T2u, T2g), fourfold (Gu, Gg), and fivefold (Hu, Hg) degenerate irreducible representations of a regular icosahedron.
As originally established by Jahn and Teller in “Stability of Polyatomic Molecules in Degenerate Electronic States. I. Orbital Degeneracy,” Proceedings of the Royal Society A, Vol. 161, 1937, pp. 220-235: Nonlinear nuclear configurations are not suitable for a stable orbitally-degenerate electronic state. It is quite significant that the orbital degeneracy considered by Jahn and Teller explicitly excluded a degeneracy due to spin. The bonding and antibonding orbitals of icosahedral boron manifestly involve nonlinear orbitally-degenerate electronic states. The Jahn-Teller effect results in a symmetry-breaking which lifts electronic orbital degeneracies by normal displacements of the 12 nuclei, known as Jahn-Teller-active modes, that distort polyatomic ions and molecules. The vibrational Jahn-Teller-active modes can be described in terms of the same irreducible representations as the electronic state, such that the vibrational state can be specified in terms of the irreducible representations of a regular icosahedron.
In the known boron-rich solids, the icosahedral symmetry is broken and the boron icosahedra are distorted by the Jahn-Teller effect. Most boron-rich solids in the prior art act as inverted molecular solids in which intericosahedral bonds are stronger than the intraicosahedral bonds. Icosahedral boron-rich solids are often referred to as inverted molecules. What is needed in the art is a genus of icosahedral boron-rich solids in which icosahedral symmetry is preserved. Such materials potentially offer electronic properties that are at least as important as those found in graphene, with the further capability of being compatible with monocrystalline silicon using standard manufacturing techniques. An excellent survey of boron-rich solids is given by Emin in “Unusual properties of icosahedral boron-rich solids,” Journal of Solid-State Chemistry, Vol. 179, 2006, pp. 2791-2798.
There potentially exists a novel form of boron capable of overcoming limitations of the recently discovered allotropes of carbon comprising the fullerenes, carbon nanotubes, and graphene. Although the study of graphene has advanced the general understanding of quantum electrodynamics in condensed matter physics, inherent limitations in its structure and, indeed, the structure of the allotropes of carbon, hinder practical applications. Chief among such limitations is an inability to combine these materials with monocrystalline silicon, on which the electronics industry has been built. Boron, which sits adjacent to carbon on the periodic chart, provides an alternative bridge between quantum electrodynamics and condensed matter physics, with an added benefit that, by carefully controlling its form, it can be integrated with silicon in a highly novel picocrystalline polymorph.